Related papers: Compressed word problems in HNN-extensions and ama…
For a fixed $n\ge2$, the Houghton group $H_n$ consists of bijections of $X_n=\{1,\ldots,n\} \times \mathbb{N}$ that are `eventually translations' of each copy of $\mathbb{N}$. The Houghton groups have been shown to have solvable conjugacy…
In this survey we show how well known results about the Word Problem for finite group presentations can be generalized to the Word Problem and other decision problems for non-necessarily finite monoid and group presentations. This is done…
We find bounds on the Hilbert space compression of the limit of a directed metric system of groups. We also give estimates on the Hilbert space compression of group extensions of a group $H$ by a a word-hyperbolic group or a group of…
We find a general family of selfless inclusions in reduced amalgamated free products of C*-algebras. Apart from generalizing prior works due to McClanahan, Ivanov and Omland, our work yields a few other applications. We present a short new…
Constraint Satisfaction Problem on finite sets is known to be NP-complete in general but certain restrictions on the constraint language can ensure tractability. It was proved that if a constraint language has a weak near unanimity…
We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…
It is known that the spatial product of two product systems is intrinsic. Here we extend this result by analyzing subsystems of the tensor product of product systems. A relation with cluster systems is established. In a special case, we…
Zimin words are very special finite words which are closely related to the pattern-avoidability problem. This problem consists in testing if an instance of a given pattern with variables occurs in almost all words over any finite alphabet.…
We prove that the generalised word problem of a finitely generated subgroup of a finitely generated virtually free group is context-free, that a hyperbolic group must be virtually free if it has a torsion-free quasiconvex subgroup of…
A reduction formula for compressions of von Neumann algebras arising as free products is proved. This shows that the fundamental group is all of the positive reals for some such algebras. Additionally, by taking a sort of free product with…
We consider the class of groups whose word problem is poly-context-free; that is, an intersection of finitely many context-free languages. We show that any group which is virtually a finitely generated subgroup of a direct product of free…
A longstanding question of Gromov asks whether every one-ended word-hyperbolic group contains a subgroup isomorphic to the fundamental group of a closed hyperbolic surface. An infinite family of word-hyperbolic groups can be obtained by…
We prove a long exact sequence in KK-theory for both full and reduced amalgamated free products in the presence of conditional expectations. In the course of the proof, we established the KK-equivalence between the full amalgamated free…
Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT($\cdot$) problem…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
The power word problem for a group $G$ asks whether an expression $u_1^{x_1} \cdots u_n^{x_n}$, where the $u_i$ are words over a finite set of generators of $G$ and the $x_i$ binary encoded integers, is equal to the identity of $G$. It is a…
Let $G$ be the generalized free product of two groups with an amalgamated subgroup. We propose an approach that allows one to use results on the residual $p$-finiteness of $G$ for proving that this generalized free product is residually a…
We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.
We isolate a tractable class of HNN-extensions of a free group, namely, multiple HNN-extensions by basis-conjugating embeddings. For this class, we construct a normal form and establish a practical version of the ping-pong lemma that…
This paper gives necessary and sufficient conditions that the free product with amalgamation of circularly-ordered groups admit a circular ordering extending the given orderings of the factors. Our result follows from establishing a…